Question Detail
Question
Evaluate lim(x→3) (x⁴-81)/(x³-27)
Correct Answer
Option B is the correct answer.
Detailed Explanation
Factor both: x⁴-81=(x-3)(x³+3x²+9x+27) and x³-27=(x-3)(x²+3x+9). Cancel (x-3) and substitute x=3: (27+27+27+27)/(9+9+9)=108/27=4.
Hint
Both expressions share the factor (x-3); factor it out of each before substituting.